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A028933 Table of winning positions in Tchoukaillon (or Mancala) solitaire. 6
0, 1, 0, 2, 1, 2, 0, 1, 3, 1, 1, 3, 0, 0, 2, 4, 1, 0, 2, 4, 0, 2, 2, 4, 1, 2, 2, 4, 0, 1, 1, 3, 5, 1, 1, 1, 3, 5, 0, 0, 0, 2, 4, 6, 1, 0, 0, 2, 4, 6, 0, 2, 0, 2, 4, 6, 1, 2, 0, 2, 4, 6, 0, 1, 3, 2, 4, 6, 1, 1, 3, 2, 4, 6, 0, 0, 2, 1, 3, 5, 7, 1, 0, 2, 1, 3, 5, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Table read by rows where b(n,i) = the number of counters in the i-th position from the store of the unique winning Tchoukaillon board having n total counters.

LINKS

Table of n, a(n) for n=0..87.

D. Betten, Kalahari and the Sequence "Sloane No. 377", Annals Discrete Math., 37, 51-58, 1988.

D. M. Broline and _Daniel E. Loeb_, The combinatorics of Mancala-Type games: Ayo, Tchoukaillon and 1/Pi, J. Undergrad. Math. Applic., vol. 16 (1995), pp. 21-36.

Brant Jones, Laura Taalman and Anthony Tongen, Solitaire Mancala Games and the Chinese Remainder Theorem, Amer. Math. Monthly, 120 (2013), 706-724.

FORMULA

Let p(n) be the minimum j such that b(n,j) = 0.  (This is A028920.)

Directly from the rules of Tchoukaillon, we find b(n+1,i) = (b(n,i) - 1 for 1 <= i < p(n), i for i = p(n), and b(n,i) for i > p(n)).

Also, b(n,i) = (n - Sum_{j=1..(i-1)} b(n,j)) mod (i+1).

EXAMPLE

   The rows of b(n,i) begin

   n\i 1 2 3 4 5 6

   1   1

   2   0 2

   3   1 2

   4   0 1 3

   5   1 1 3

   6   0 0 2 4

   7   1 0 2 4

   8   0 2 2 4

   9   1 2 2 4

   10  0 1 1 3 5

   11  1 1 1 3 5

   12  0 0 0 2 4 6

   13  1 0 0 2 4 6

   14  0 2 0 2 4 6

   15  1 2 0 2 4 6

   16  0 1 3 2 4 6

   17  1 1 3 2 4 6

MATHEMATICA

s[list_] := Module[{x = Append[list, 0], i = 1}, While[x[[i]] =!= 0, x[[i]] = x[[i]] - 1; i = i + 1]; x[[i]] = i; If[Last@x == 0, Most[x], x]]; Prepend[Flatten@NestList[s, {}, 20], 0] (* Birkas Gyorgy, Feb 26 2011 *)

CROSSREFS

Cf. A002491, A028920, A007952, A028931, A028932, A028933.

Sequence in context: A063574 A144515 A178650 * A190491 A143352 A127170

Adjacent sequences:  A028930 A028931 A028932 * A028934 A028935 A028936

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Formulas added by Brant Jones, Oct 14 2013

STATUS

approved

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Last modified February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)